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Renormalization of Symmetric Bimodal Maps with Low Smoothness

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Abstract

This paper deals with the renormalization of symmetric bimodal maps with low smoothness. We prove the existence of the renormalization fixed point in the space \(C ^{1+Lip}\) symmetric bimodal maps. Moreover, we show that the topological entropy of the renormalization operator defined on the space of \(C^{1+Lip}\) symmetric bimodal maps is infinite. Further we prove the existence of a continuum of fixed points of renormalization. Consequently, this proves the non-rigidity of the renormalization of symmetric bimodal maps.

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Acknowledgements

The authors would like to thank the referees for the useful comments and suggestions to improve the manuscript. We are grateful to the referees for their valuable remarks.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology, Jodhpur, Rajasthan, 342037, India

    Rohit Kumar & V. V. M. S. Chandramouli

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  1. Rohit Kumar
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  2. V. V. M. S. Chandramouli
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Correspondence to V. V. M. S. Chandramouli.

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Communicated by Peter Balint.

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Kumar, R., Chandramouli, V.V.M.S. Renormalization of Symmetric Bimodal Maps with Low Smoothness. J Stat Phys 183, 29 (2021). https://doi.org/10.1007/s10955-021-02764-8

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